Series and Parallel Circuits
Current, Potential Difference and Resistance
Electric current is the rate of flow of charge. In a metal conductor, it is the movement of free electrons driven by a power supply. Current (symbol \(I\)) is measured in amperes (A) using an ammeter connected in series.
Potential difference (symbol \(V\), measured in volts) is the work done per unit charge as it moves between two points in the circuit. It is the ‘push’ that drives current around the circuit. A voltmeter measures potential difference and is connected in parallel across a component.
Resistance (symbol \(R\), measured in ohms, \(\Omega\)) is the opposition to current flow. For many components at constant temperature, current is proportional to potential difference — this is Ohm’s law: $$V = I \times R$$
Potential difference \(V\) = current \(I\) × resistance \(R\). Units: volts = amperes × ohms. Rearranged: \(I = V / R\) and \(R = V / I\). This applies to resistors at constant temperature (ohmic conductors).
Series Circuits
In a series circuit, there is only one path for the current. This means the current is the same through every component. The total potential difference of the power supply is shared between all the components: the component with the greatest resistance receives the largest share of the voltage. If one component in a series circuit breaks, the circuit is incomplete and all components stop working.
The total (equivalent) resistance in a series circuit is simply the sum of all the individual resistances: $$R_{\text{total}} = R_1 + R_2 + R_3 + \ldots$$ Adding more resistors in series increases total resistance and reduces current.
Question: Two resistors of 4 Ω and 6 Ω are connected in series with a 10 V battery. Calculate (a) the total resistance, (b) the current in the circuit, and (c) the potential difference across the 4 Ω resistor.
(a) Total resistance: \(R_{\text{total}} = 4 + 6 = 10\) Ω
(b) Current: Using \(I = V / R\): \(I = 10 / 10 = 1\) A. This current is the same through every component.
(c) PD across 4 Ω resistor: \(V = I \times R = 1 \times 4 = 4\) V. (Check: the remaining 6 V appears across the 6 Ω resistor; 4 + 6 = 10 V ✓)
Parallel Circuits
In a parallel circuit, there are multiple branches. Each branch has the same potential difference across it (equal to the supply voltage). Current splits between the branches: more current flows through branches with lower resistance. If one branch breaks, current still flows through the other branches.
Adding more resistors in parallel gives more paths for the current, so total resistance decreases. This is often misunderstood — students sometimes assume that more components always means more resistance. In parallel, the opposite is true: total resistance is less than the smallest individual resistance.
Series: same current everywhere; voltage shared in proportion to resistance; total resistance = sum of all resistances. Parallel: same voltage across each branch; current splits (more through lower resistance); total resistance is less than the smallest branch resistance.
I-V Graphs and Non-Ohmic Components
For an ohmic resistor (one whose resistance stays constant), the I-V graph is a straight line through the origin — doubling the voltage doubles the current. Some components are non-ohmic: their resistance changes with current or conditions.
A filament lamp has an I-V graph that curves — as current increases, the filament gets hotter, its resistance increases, so the current does not increase as fast. A diode only allows current to flow in one direction: its I-V graph is nearly flat (almost zero current) for reverse voltage and rises steeply for forward voltage above a threshold. A thermistor has a resistance that decreases as temperature rises. A light-dependent resistor (LDR) has a resistance that decreases as light intensity increases.
A very common error is to say that ‘current is used up’ as it passes through components in a series circuit. This is incorrect. Current (the flow of charge) is the same everywhere in a series loop. What changes around a series circuit is the potential difference (voltage) — each component causes a voltage drop proportional to its resistance. It is energy that is transferred to the components, not charge. Charge flows continuously in a loop, returning to the battery to be given more energy.
A helpful analogy is a water circuit: the pump (battery) pushes water (charge) around a loop through a series of turbines (resistors). The water speed (current) is the same everywhere in the loop; the water gives up pressure (potential difference) at each turbine; but the same water returns to the pump. In a parallel water circuit, the flow splits into multiple channels — each channel has the same pressure drop, but less water flows through each individual channel than in the equivalent series arrangement.